We colloquially refer to sodium chloride as “salt” and it leads many people to associate the word salt with food. For everyday purposes, that meaning is perfectly fine. However the word “salt” as used in chemistry simply means a neutrally charged compound consisting of positive cation(s) and negative anion(s). Sodium chloride (NaCl, or Na ^+ Cl ^- ) meets this criteria, hence it being called salt.

The same chemical definition fits amphetamine salts and the formulation of lithium used clinically, however that’s the end of their similarity with food items. When using these medications, it isn’t the fact that patients get a “salt” that’s causing a clinical change, but rather that the medications have specific mechanisms of action (e.g. Lithium reduces excitatory stimulation of dopamine and glutamate and up-regulates GABA, though it’s actual mechanism of action is largely unknown).

That doesn’t mean that diet could not, or does not, affect mental health disorders, just that diet’s effect is a completely different topic.